Algorithms of Fast Adaptive Compensation of Disturbance in Linear Systems with Arbitrary Input Delay

Abstract

The problem of fast compensation of multisinusoidal disturbance affecting on linear time-invariant (LTI) plants with known parameters and arbitrary input delay is considered. The disturbance is modeled as unmeasurable bounded output of linear exosystem of known order but with unknown parameters. Disturbance compensation is provided by means of direct adaptive control with two schemes of adaptation algorithm. The first scheme is based on the standard gradient adaptation algorithm, while the second one uses modified adaptation algorithm with integral cost function and improved parametric convergence. The stability of the closed-loop system in presence of delay and integral action (due to direct adaptation) in the feedforward loop is ensured by appropriate modifications of the adaptation schemes. These modifications allow to remove the limitations on upper bounds on adaptation gains (gain margins) corresponding to certain upper bounds of time delays (delay margins). The performance of proposed schemes of disturbance compensation is demonstrated via simulation.